Calendar

For a moduli space $M$ of stable sheaves over a K3 surface $X$, we propose a series of conjectural identities in the Chow rings $CH_\star (M \times X^\ell),\, \ell \geq 1,$ generalizing the classic Beauville–Voisin identity for a K3 surface. We emphasize consequences of the conjecture for the structure of the tautological subring $R_\star (M) \subset CH_\star (M).$ We prove the proposed identities when $M$ is the Hilbert scheme of points on a K3 surface. This is based on joint work with L. Flapan, A. Marian and R. Silversmith.

I will construct LG mirrors for the Johnson-Kollár series of anticanonical del Pezzo surfaces in weighted projective 3-spaces. The main feature of these surfaces is that their anticanonical linear system is empty. Thus they fall outside of the range of the known mirror constructions. For each of these surfaces, the LG mirror is a pencil of hyperelliptic curves. I will exhibit the regularised I-function of the surface as a period of the pencil and I will sketch how to construct the pencil starting from a work of Beukers, Cohen, and Mellit on finite hypergeometric functions. This is joint work with Alessio Corti.

**CANCELED**

Most 4-manifolds do not admit symplectic forms, but most admit 2-forms that are “nearly” symplectic. Just like the Seiberg-Witten (SW) invariants, there are Gromov invariants that are compatible with the near-symplectic form. Although (potentially exotic) 4-spheres don’t admit them, there is still a way to bring in near-symplectic techniques and I will describe my ongoing pseudo-holomorphic attempt(s) at analyzing them.

We provide a new parton theory for hole doped cuprates. We will describe both a pseudogap metal with small Fermi surfaces and the conventional Fermi liquid with large Fermi surfaces within mean field level of the same framework.  For the pseudogap metal,  “Fermi arc” observed in ARPES can be naturally reproduced.  We also provide a theory for a critical point across which the carrier density jumps from x to 1+x.   We will also discuss the generalization of the theory to Kondo breaking down transition in heavy fermion systems and  generic SU(N) Hubbard model.

There is a large literature about points of bounded height on varieties, and about number fields of bounded discriminant. We explain how to unify these two questions by means of a new definition of height for rational points on (certain) stacks over global fields. I talked about some aspects of this work at Barry’s birthday conference, and will try in this talk to emphasize different points, including a conjecture about the asymptotic counting function for points of bounded height on a stack X which simultaneously generalizes the Manin conjectures (the case where X is a variety) and the Malle conjectures (the case where X is a classifying stack BG.)